General integral relations for the description of scattering states using the hyperspherical adiabatic basis

In this work we investigate 1+2 reactions within the framework of the hyperspherical adiabatic expansion method. To this aim two integral relations, derived from the Kohn variational principle, are used. A detailed derivation of these relations is shown. The expressions derived are general, not restricted to relative $s$ partial waves, and with applicability in multichannel reactions. The convergence of the ${\cal K}$-matrix in terms of the adiabatic potentials is investigated. Together with a simple model case used as a test for the method, we show results for the collision of a $^4$He atom on a \dimer dimer (only the elastic channel open), and for collisions involving a $^6$Li and two $^4$He atoms (two channels open).Comment: Accepted for publication in Physical Review

Variational description of continuum states in terms of integral relations

Two integral relations derived from the Kohn Variational Principle (KVP) are used for describing scattering states. In usual applications the KVP requires the explicit form of the asymptotic behavior of the scattering wave function. This is not the case when the integral relations are applied since, due to their short range nature, the only condition for the scattering wave function $\Psi$ is that it be the solution of $(H-E)\Psi=0$ in the internal region. Several examples are analyzed for the computation of phase-shifts from bound state type wave functions or, in the case of the scattering of charged particles, it is possible to obtain phase-shifts using free asymptotic conditions. As a final example we discuss the use of the integral relations in the case of the Hyperspherical Adiabatic method.Comment: 34 pages, 7 figures, accepted in Phys. Rev.

Integral relations for three-body continuum states with the adiabatic expansion

Application of the Hyperspherical Adiabatic expansion to describe three-body scattering states suffers the problem of a very slow convergence. Contrary to what happens for bound states, a huge number of hyperradial equations has to be solved, and even if done, the extraction of the scattering amplitude is problematic. In this paper we show how to obtain accurate scattering phase shifts using the Hyperspherical Adiabatic expansion. To this aim two integral relations, derived from the Kohn Variational Principle, are used. The convergence of this procedure is as fast as for bound states.Comment: 4 pages, 1 figur

Optimal network topologies for local search with congestion

The problem of searchability in decentralized complex networks is of great importance in computer science, economy and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and obtain expressions for the average search cost--written in terms of the search algorithm and the topological properties of the network--both in presence and abscence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: star-like configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when the number of parallel searches is large.Comment: 4 pages. Final version accepted in PR

The helium trimer with soft-core potentials

The helium trimer is studied using two- and three-body soft-core potentials. Realistic helium-helium potentials present an extremely strong short-range repulsion and support a single, very shallow, bound state. The description of systems with more than two helium atoms is difficult due to the very large cancellation between kinetic and potential energy. We analyze the possibility of describing the three helium system in the ultracold regime using a gaussian representation of a widely used realistic potential, the LM2M2 interaction. However, in order to describe correctly the trimer ground state a three-body force has to be added to the gaussian interaction. With this potential model the two bound states of the trimer and the low energy scattering helium-dimer phase shifts obtained with the LM2M2 potential are well reproduced.Comment: 15 pages, 3 figures, submitted to Few-Body System

The Intrinsic Fundamental Group of a Linear Category

We provide an intrinsic definition of the fundamental group of a linear category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the Galois group of the universal covering. The grading deduced from a Galois covering enables us to describe the canonical monomorphism from its automorphism group to the first Hochschild-Mitchell cohomology vector space.Comment: Final version, to appear in Algebras and Representation Theor

Phenomenological Models of Socio-Economic Network Dynamics

We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is defined by the particular process taking place on the network. The interplay between the two processes produces phase transitions and hysteresis, as seen using numerical simulations for three specific processes. We obtain analytic results using mean field approximations, and for a particular case we derive an exact solution for the network. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence.Comment: 11 pages, 8 figure

Analytical simulation of RBS spectra of nanowire samples

Almost all, if not all, general purpose codes for analysis of Ion Beam Analysis data have been originally developed to handle laterally homogeneous samples only. This is the case of RUMP, NDF, SIMNRA, and even of the Monte Carlo code Corteo. General-purpose codes usually include only limited support for lateral inhomogeneity. In this work, we show analytical simulations of samples that consist of a layer of parallel oriented nanowires on a substrate, using a model implemented in NDF. We apply the code to real samples, made of vertical ZnO nanowires on a sapphire substrate. Two configurations of the nanowires were studied: 40 nm diameter, 4.1 μm height, 3.5% surface coverage; and 55 nm diameter, 1.1 μm height, 42% surface coverage. We discuss the accuracy and limits of applicability of the analysisAuthors thank funding from projects CTQ2014-53334-C2-2-R (MINECO, Spain) and NANOAVANSENS S2013/MIT 3029 (Comunidad de Madrid). A.R.C. acknowledges Juan de la Cierva program (under contract number JCI-2012-14509). This work was partially funded by Fundação para a Ciência e Tecnologia under grant UID/Multi/04349/201

Breakdown of anomalous channeling with ion energy for accurate strain determination in gan-based heterostructures

The influence of the beam energy on the determination of strain state with ion channeling in GaN-based heterostructures (HSs) is addressed. Experimental results show that anomalous channeling may hinder an accurate analysis due to the steering effects at the HS interface, which are more intense at lower ion energies. The experimental angular scans have been well reproduced by Monte Carlo simulations, correlating the steering effects with the close encounter probability at the interface. Consequently, limitations in the determination of the strain state by ion channeling can be overcome by selecting the adequate beam energy